Our main topic is the forward utility field, which is quite a new concept introduced by Musiela and Zariphopoulou. Different from most articles in this field discussing forward utility in a continuous market, we extend this concept to jump market case. We first provide a generalized Itô- Ventzell formula, which can be applied in a general jump semimartingale driven by Brownian motion and Poisson random measure. Three special forward utility models are discussed by exploiting this generalized Itô-Ventzell formula.